Example of a topological space that is connected, not locally connected and not path connected

Question

I know that "The topologist's sine curve" is an example of a topological space that is connected, not locally connected and not path connected.

https://en.wikipedia.org/wiki/Topologist%27s_sine_curve

What would be another "simpler" example that meets these properties?

Answer 1

The comb space is an example with similar properties to the topologists sine curve... See https://en.m.wikipedia.org/wiki/Comb_space.

In particular, the deleted comb space has the properties you require...

Answer 2

Searching π-Base for (Connected + ~Path Connected + ~Locally Connected), we get:

Pointed Rational Extension of $\mathbb{R}$
Pointed Irrational Extension of $\mathbb{R}$
Indiscrete Rational Extension of $\mathbb{R}$
Indiscrete Irrational Extension of $\mathbb{R}$
An Altered Long Line
The Infinite Cage
Smirnov's Deleted Sequence Topology
Irrational Slope Topology
Roy's Lattice Space
Topologist's Sine Curve
Closed Topologist's Sine Curve
Cantor's Leaky Tent
The Infinite Broom
One Point Compactification of the Rationals
Nested Angles

Perhaps the one-point compactification of $\mathbb Q$ is the simplest example.